With time running out, Congress returns Monday to try to pass a short-term funding measure to avert a government shutdown and avoid yet another market-rattling showdown over the federal budget.

The Democratic-led Senate, which on Friday blocked a GOP House measure to fund the government through Nov. 18, will vote late Monday on its own version of the bill.

The Senate bill includes dollars for disaster relief without an offsetting spending cut elsewhere that the House GOP demands.

It is not clear how the dispute will be resolved. A spokesman for House Speaker John A. Boehner (R-Ohio) said Sunday that leaders have been in touch, but other congressional aides said there was no progress toward a compromise over the weekend.

And members of Congress who appeared on Sunday talk shows gave little sign that they would move quickly from their parties’ positions on disaster relief.

“The Senate is saying . . . why should we, in effect, rebuild schools in Iraq on the credit card but expect that rebuilding schools in Joplin, Missouri, at this moment in time have to be paid for in a way that has never been in any of the previous disaster assistance that we’ve put out before?” Sen. Mark R. Warner (D-Va.) said on CNN’s “State of the Union.” He blamed the dispute on tea-party-affiliated Republicans in the House who demanded the spending cut.

Sen. Lamar Alexander (R-Tenn.) said on the same program: “Everybody knows we’re going to pay for every single penny of disaster aid that the president declares and that FEMA certifies. And the House sent over a bill that does that and the Senate should have approved it.”

But Warner and Alexander, who have been pushing for more bipartisan cooperation over the far more difficult and consequential task of deficit reduction, appeared weary over the mess. Warner called it “embarrassing.”

“I don’t like this business of sitting around blaming each other over such small potatoes,” Alexander said.

But the small potatoes are part of a much larger and ongoing fight about debt and deficit spending in Washington.

Last week, Boehner lost a vote on how to fund the federal government, sending Washington bumbling into its third shutdown showdown in the past six months.

His problem was the same as in the previous spending battles — roughly 50 of the most conservative Republicans who mutinied in the name of deeper spending cuts.

But Boehner may have strengthened his hand in the fight by persuading his fractious team to rally around his leadership.

The fact that a resolution now hinges on action in the Senate is a sign that Boehner is in stronger position politically than he was a week ago — that he can now sometimes harness the power of his majority, despite nine months of often chaotic rule.

Rather than working with Democrats, he worked on Republicans, persuading enough to switch their votes. The House passed an almost identical version of the spending bill Thursday and forced the issue to the Senate.

Boehner has had to rely on temporary and unstable coalitions to achieve victories, often won with bluffs and brinkmanship against a deadline of impending doom.

Last week, he built one with Republicans. This week, he may be forced to turn to Democrats. Without the full strength of his majority behind him, that has been Boehner’s go-to in the past — tricky arrangements that have required him to win three-quarters of the votes of Republicans but still keep nearly half of Democrats on board.

What appeared in the end to persuade the reluctant GOP members who switched last week was not arm twisting or legislative pressure tactics that were once famous in the House, but something else entirely: logic.

Leaders argued that if members wanted to cut spending, voting for the measure was their only viable option.

The alternative was to require Boehner to negotiate with Democrats on a bill that would not offset any of the $3.65 billion Republicans had agreed to set aside for FEMA and other disaster relief efforts.

In other words, voting against the bill in hopes of forcing government to spend less would actually result in spending more.

“He said you have to pick — and they picked,” said Rep. Steven C. LaTourette (R-Ohio), a close ally of Boehner’s. “It’s too bad we had to have the vote and lose, but I think people came to the right conclusion pretty quickly.”

One key moment came in a closed-door meeting Thursday for House Republicans, when Rep. Dana Rohrabacher (R-Calif.) rose to his feet and acknowledged that he had planned to support the bill the night before but decided to vote against it when he saw it was headed for defeat.

It was cowardly, he said. If given another opportunity, he promised to stick by Boehner and vote “yes.”

King said people laughed. Then others acknowledged they had done the same.

“He saw it was going to go down anyway, so he could take the easy vote and vote ‘no’ and be a hero to the people back home to people who wanted more cuts,” King said.

Slowly but surely, Republican leaders are persuading freshman elected last year on promises to remake Washington that there’s more to being an effective congressman than heroics for the folks back home.

“I think the speaker and the leader are trying to get that across,” King said. “I think it is starting to sink in.”

The message worked on some.

Rep. Jeffrey M. Landry (R-La.), who had voted against the bill Wednesday, said he was persuaded to support the bill a day later by the argument that his “no” vote would help produce a bill with higher spending.

“That would have been a bill that I wouldn’t have supported but Americans would likely have had to live with,” he said.